Why does a child in a wagon seem to fall backward when you)x1i6jvr1hsg t7s r5sxv0 q0 q give the wagon a sharp pullvh q7 01x s)vr1q6x5sj0sit gr forward?

A box rests on the (frictionless) be4 o 19vhn5v)wzz 3febpd of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truw5ezob )fvzh 14n 3p9vck and (b) by Chris who is riding on the truck

If the acceleration w zc7 ;*v 3e2,htmmuy:h2g 7)lz hvresof an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Cang*bex 1nfn/ dss b4:mm0e-mh. the object have zero acceleration? Can it have zero velocith4 sbmfm .g m-1 /de*nn0bxse:y? Explain.

When a golf ball is dropp4ga zrrsom1 *:l7- m3bsfyh;t(, 0ilaxd a7bped to the pavement, it bounces back up. (a) Is a force needed to make it bouazgrl1,x7a3 i0s mb7 -*p aml4sdtybor(hf:;nce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move inx046)t uvljsxe) g(vo yy;o(g the opposite d v t l)v(xy(6soe)0y;gx u4jogirection?

Why might your foot hurt if u.jr+y5j3vs+ad -ldw you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. q)jc94ms 3c*05 hsws)szge) cfh kv d;(a) Wh mc q)e;s zh)s)wjd35fskcc*hvg9s 4 0at is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same th kfsuw jbk;wo3xq0/ d2 8h:fu-read dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on th8sfw2b3jwk0hk-u : /foux; dqe dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a / o5i3l+jnllol(fe) y2-kg rock is twice as great as that on a 1-kg rock. Whynjlyi +l5) ol(3/fo el then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give ac*okjdh5w4qi e. 7hv i4curate results if the scale had been calibrated (a) in qj khvhwi54*do e7 .i4pounds, or (b) in kilograms?

You pull a box with a constanyezror 9s5,u23+xh qxt force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontaxrx2+q e9ys5, uo3r zhl (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there ib +88abbxa4m(vzo h:ks a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Eart vab8o(zbxa4h b:m8+k h. Why doesn’t the Earth move?

Compare the effort (or forcety y.)n ;tu9dw) needed to lift a 10-kg object when you are on the Moon .)ndy;t 9yu twwith the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team izl(o,v hgti )8n a tug of war (Fig. 4–37) pulls with equal for8t,h )ziol(v gce on the other team. What, then, determines which team will win?

A person exerts an upz 0vzv)ml.v (ooj-oc 8ward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) j8z .)-oo0 c(ozlvvmv by what object it is exerted.

When you stand still on the ground, how large a force does the ground xe+dm3xev7 ;u exert on you? Why doesn’t this force make you rise u xumed xv;+3e7p into the air?

Whiplash sometimes results from an automobile acci8 m,s6 qn tdiji 0djw+m;il/i3dent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situatioi,diinlj6mdm s /w+jt i80;3qn. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck ac quo1m) s*k)ett0ph5f celerates, the crate remains where it is on the truck, so it, too, accelerates. What fkse)pou1ft 5 t)m0 *qhorce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After they adplzx,5h)p):dqpr46vmz ) block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent tha4yp5)x)zd6 pmz)hqdrvalp : ,n on the ascent. Why?

What would your bathroom +ce:jl ew8ah co81(byt 93rqru0u 2 soscale read if you weighed yourself on an inclined plane? Assume the mechanismo8eoa2r su(9810wujblt h:r ec3c q+y functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/smvz.:6bo p; dj$^2$?   

  A net force of 265 N accelerates a bikexr7cwdvy7e z1 d 5(9(/i 9vwidjbz+p e and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand i/jbi;fyu: cw* f it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a at x77k- r/zd3kd4thz $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the car il ze- 04/o tf fwx:b4zyz0h2a7d:kxqkpf+z. ls traveling at 95km/40htz q: zzk+afowf:l2 p/0zlb x47 xdef y-.kh? -  

  What average force is needed to acc) sq1xay5u9-j p(xybll+hus 9elerate a 7.00-gram pellet from rest to 125m/s over a distance oxsy9lux9-b(l hp jayu1q5+s) f 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically h-q*vkp w;zy7:s/ kxdout of the water with an acceleration of 2.5 x; 7:-v*yh/s d kpzwqk$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (7hb. urf jz73i402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximuad)r65f k9mj em acceleration is 0.0680 g . What are the maximum anj) fekdam65r9d minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless elevator. When wb y vln88o(n:-,1 etr0g0iu0kecpyy the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the di8gic-,0(rtyoyw e0 y8lu1n0 ek:pb v nrection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a 7 ool.xsayyy e7v)7ah( bi2( vmaximum strength of 21,750 N. What maximum upward acceleration can it give the elevator withoutye7 xvao7 il(ah. 2v bs)yyo7( breaking?    ( two decimal places)

  (a) What is the acceleration of tw uhyjf2z53 9jno falling sky divers (mass 132 kg including parachute) whenuyfjnhj5z9 23 the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he st7bqz jvzp2z q1 x9f(w7rikes the ground below, he bends his knees so that his torso decelerates oveq( 91f b2zvpzwzqj 7x7r an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tiedzf-drfz 7, tkky0:e6q to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-4rqtfe07:zkfd ,yz-6k 0). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram ;kytfb t 8qzhe3dpa-.;gt4p8for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment itv9s0qtxkyq27degv:(j( y z- i is hit by the bat, aj k( qs:xqydtzy2v0i -e9(7vgnd again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be etu 4g;zsml;( bk ;rbh,xerted in what directio,bh;ls (ur tbk4g; zm;n so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontauo-4+35jo q l73.f fqazigosmlly between two buildings 10.0 m apart. The sagf4sj75ooq a+-3qz lif mg. o3u in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a z xwzna r )f/qg6b*9o(massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.d uq2uoi(,f,1 xa9 o3 hnvq3vd0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit tomixasfe 2i (it ma5oai8h5/) . a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces m8if5aoa2i)i e(/.xmits h 5 a$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the sa+ 6n1ek 9bxr(z6kwkoome mass behind it, Fig. 4-47 . Determine the ratio of +(kkk6wne6x b1 roo 9zthe tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using thej:pfw go4 xvsm8 g-uyri2fl3l 6 5s4-e bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must syjw :s3fl f pxlo6v44 r- gge5ms8ui-2he pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a rac +o)o1 hibdhc*r(nyk4 e began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a bpux981nlns46o( nj bmn 8u vort8;i , 7kfe8rclock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless vymo2c*kn a+ot81* +j quq(g ohorizontal surface are in contact with each other, as shown in Fig. 4-o+y +qc uo (nm1* 8gqtjoa2vk*51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m abo;efteh:*i( xa ve the ground, and the massless frictionlefetha *iex;( :ss pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are cod,8rraqahxupjtp5g 2ju, qmy3. :,8d nnected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig.ag3p8 .qpmrd,u8jyr ajt : ux ,dqh25, 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between apzs6 rjrqs: glv(19*r 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is requireaig:dgxc 3 6*jr xa+h-d to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating 9(oivp4 c p,keat 0.20g. What minimum coefficient of static friction must ex4ecipp o k,9v(ist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can +7ajccu/cjufo qt-s:6 /;htc undergo if the coefficient of static friction betwoqt; c/jc6:ah/t +cuc7s -fuj een the tires and the ground is 0.80?   

  The coefficient of static friction betv-tveh bl,)79 4ythvsween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you lh9stv,ve ) tyh7bl4-veave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.80 q5ej **j r0xa3trhk6b$\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest o0 a ltz- b*8 s*nl5f,jeobo0dsn a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a vbsy1upukj, 7ttl- py0 w v8(1cery high coefficient of static frwultk 1t pjv8us (7-p,1cyby0iction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic fri(v 2+0ensdmmi ction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Examghu 78eo osn*364 qmubr mh/t6ple 4-20) how large a mass would box A have to have to prevent any motion from occurring? Asnuhrs7ob qt6*m3hu4o8 6e/mgsume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so tu i6n-tvqi-9vask1s 3 hat it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the ps s-uqn1viiat 39v-k 6ush imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a ho8wj sqt 8)yaq(rizontal surface (Fig. 4-54ws)y( aqq8jt8 ). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crod ,.urk: .duwate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver ca, kdw: ru.d.oun decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you wo;xce8xeg/ 5 0ukdy/kt( pif9 d:9 ekanrry about parking your car in your driveway, which has an incliput/ex exfnd 9 y05a9 (/kd kkg:8ic;ene of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with zlo*msnu 7o- 4 kpp9f9a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted abj); gvo8a 58k6 o;jf 0ssuenht an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial spenag kw6c+ql+ (6geow 7ed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a 3)zw5i ;5;rw hfndfgdlp7h*tspeed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rougg.u -nsnmyte*ib xl(1.f pa2l + qf/g(h wall by someone pushing on it with a forcb .ag*nf1 lxmfgpi l2(t-u+s .y/neq( e directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can .qzxl m8vgzwd1fius) 7r4z 5 wr -8l2ebecome dangerous projectiles as they melt. Consider a chunk of snow at the ridge 52-)m qrsivwzelz 8ul1 w .78 dfxzrg4of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an aut ;vb 03vbdbfd/omobile traveling at speed b/bvvbd;f0 d3v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drive )c/mk sgi6mu- 1m(xmerm/ksim-6() eu1 mmcxg decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an 7+ rxs2p4+h lmmny5 l;xdou9k initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where + ktag88npzdtpk8 nc1+gj.ig 3.dx(m they are filled to the packing station 11.0 m away. Th++(jgdckgt.ima38ndnpk 1x gp.t8z 8 e belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of5l01 bjsk8ad 0trdl nrj54rmyc.r95 o kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg ,a qcdva,ky, 0(including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a m *j;c 9 r0hobv9mql vy)czbp(9ammalian heart, at each pulse approximately 20 g of blood is accelerated f99y(0bp bz;cj) *chol9q rmvvrom 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable g*iy3,;niku, 7f bmndchance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Cal; ni y,3imgnd,*bu k7fculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an ex r1qz+sn 040fqe9a1h.a nlj yarthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with thehy sfqq9n a.1xa4e0r lz+01nj ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of aapd / ws(7,xodn accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before,wx 7oa/dsd( p colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling do 4x5pjbf0sej /wn a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road,e5p4 j/x0 bjfs the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning T+f 8wheq8cgn)ower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forc 8en+8h)g fwcqe of air resistance?   

  A cyclist is coasting at a steady speed ohzk,m ir t0v*9f 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. W0*,r9 mzk hvtiill the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working svepa)x+;reike7+s o /3d1 tj on the redesign of a hilly portion of a city. An important consideration is how steep the roadsix k137 vtad rs;eese+ojp)/ + can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin pi8qb2w+cuo16 if j hm ou7t1o.dece of string while the jetliner she is in takes off from JFK Airporw uqc7 mo obd 6j1oht+uf281.it (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, t/u) fbyyc vv9ba9wxnc +c+ 75ohere are to be several ramps connecting different parts of 9y5vxwa +9cb+7 nfuo / c)vcbythe store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano 0*lkdrdk9voo7 obm .o 2j g+nwl.6e-g (mass M ) using the pulley a-v oo09wr ljeo6gm bl +7kd*nkog2..d pparatus shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelx ns(9 )ousmpn3o+1nw/r6xu0oqbxx4 erating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considqv-,c pvfj:tqf 1 8(2kkjvwy2 cd +c*oers the following set of conditions:v2kj(c q:cyqvv8* kt- of,pwf12 dj+c
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (66xzhxzu8qd;*:q * 4abey; tv+f0,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safj7qu /ew4xd, rme7 s+aety ropes of similar length. Karen's rope is moresu 7awqjex +e 7/r,m4d elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is ush ,fm/ q,5+h.p *nbbdsffc. cuing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is )d3 md*h9emx42ny9yzx hkoc4allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped x4+kx*9d:u aavm4ly8 uq xvh1together are ascending an ice field inclined at 21.9+vkx:axxm4d4 1*8aqy l uvuh0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.